{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c2b7da21-f761-4b32-9b9e-f8985e2f8dc9",
   "metadata": {},
   "source": [
    "Chapter 15\n",
    "# NumPy常见运算\n",
    "Book_1《编程不难》 | 鸢尾花书：从加减乘除到机器学习  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6096674a-fdbe-4c1c-8337-03766190b08b",
   "metadata": {},
   "source": [
    "## 导入包"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "14ac1471-23c1-4f10-af2d-fb89b126430e",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb1204b2-1f67-47e5-8b6b-890e797d193d",
   "metadata": {},
   "source": [
    "## 自定义函数"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e48ac2a-1bcd-4f7e-849e-a5d35c58d82b",
   "metadata": {},
   "source": [
    "## 数学函数\n",
    "NumPy有大量数学函数，这个笔记我们仅仅选取几个常用的数学函数，并可视化函数图形。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "af0b8eb1-2132-4112-a4df-8a42de471c5d",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 自定义可视化函数\n",
    "def visualize_fx(x_array, f_array, title, step = False):\n",
    "    \n",
    "    fig, ax = plt.subplots(figsize = (5,5))\n",
    "    ax.plot([-5,5],[-5,5], c = 'r', ls = '--', lw = 0.5)\n",
    "    \n",
    "    if step:\n",
    "        ax.step(x_array, f_array)\n",
    "    else:\n",
    "        ax.plot(x_array, f_array)\n",
    "    \n",
    "    ax.set_xlim(-5, 5)\n",
    "    ax.set_ylim(-5, 5)\n",
    "    ax.axvline(0, c = 'k')\n",
    "    ax.axhline(0, c = 'k')\n",
    "    ax.set_xticks(np.arange(-5, 5+1))\n",
    "    ax.set_yticks(np.arange(-5, 5+1))      \n",
    "    ax.set_xlabel('x')\n",
    "    ax.set_ylabel('f(x)')\n",
    "    plt.grid(True)\n",
    "    ax.set_aspect('equal', adjustable='box')\n",
    "    fig.savefig(title + '.svg', format='svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "8b234d75-b778-4842-aaa7-fe05db41972c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 幂函数，p = 2\n",
    "x_array = np.linspace(-5,5,1001)\n",
    "f_array = np.power(x_array, 2)\n",
    "visualize_fx(x_array, f_array, '幂函数_p=2')\n",
    "\n",
    "# 幂函数，p = 3\n",
    "f_array = np.power(x_array, 3)\n",
    "visualize_fx(x_array, f_array, '幂函数_p=3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "73bb040f-c4d3-4959-af74-da2ae7ecfa4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "[powers]*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "c633e9f9-f6ef-4f05-b6c8-b3e6c82af19e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绝对值函数\n",
    "x_array = np.linspace(-5,5,1001)\n",
    "f_array = np.abs(x_array)\n",
    "visualize_fx(x_array, f_array, '绝对值函数')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "a7a64cec-356c-4045-8d5f-29e4d6ca1d86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 正弦函数\n",
    "f_array = np.sin(x_array)\n",
    "visualize_fx(x_array, f_array, '正弦函数')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "909e68d8-b306-43d0-ad7c-4f28b4f9a0cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 反正弦函数\n",
    "x_array_ = np.copy(x_array)\n",
    "x_array_[(x_array_ < -1) | (x_array_ > 1)] = np.nan\n",
    "f_array = np.arcsin(x_array_)\n",
    "visualize_fx(x_array_, f_array, '反正弦函数')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "842da200-e51a-46e0-8c82-c2a74cff898f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 正切函数\n",
    "f_array = np.tan(x_array)\n",
    "f_array[:-1][np.diff(f_array) < 0] = np.nan\n",
    "visualize_fx(x_array, f_array, '正切函数')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "ab58b0ce-9e6a-46fc-9d6e-89eaa1aa3d29",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 反正切函数\n",
    "f_array = np.arctan(x_array)\n",
    "visualize_fx(x_array, f_array, '反正切函数')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "015d8970-0032-499e-b4b7-9dd1fe89bf55",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 余弦函数\n",
    "f_array = np.cos(x_array)\n",
    "visualize_fx(x_array, f_array, '余弦函数')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "7a8f5e7e-90d5-4fb4-b1e4-1386aa9935fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 反余弦函数\n",
    "x_array_ = np.copy(x_array)\n",
    "x_array_[(x_array_ < -1) | (x_array_ > 1)] = np.nan\n",
    "f_array = np.arccos(x_array_)\n",
    "visualize_fx(x_array_, f_array, '反余弦函数')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "4e854ef9-545b-4890-8866-2e249945ebba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mAmtlOzGHlXKdqrGz/XfzrwBc2i3hjO9rmc/s+HmUwR06VEy9WibbKayYqz55fKosT2UYxkkjRxGRmioodvHd9lwALj3XBw6Qyc+H9HQ4w3Ea4j0+U5YTJkxg2LBhJCUlceTIEebMmcOSJUv4/PPPzY4mIj7oi037cZUZtG/RjI4tLb5wusMBzZvDffeZnSRg+UxZ7t+/n1GjRpGTk0N0dDTdu3fn888/Jz093exoIuKDFq7NAeDK7m1MTlKN+fM9WxWlqXymLP/xj3+YHUFE/ER+kYtlWz37K6/qnmBymjOYNQtuvhmuu87sJAHPZ8pSRKSh/GfjPlxlBl1aRdKpVaTZcSpXvih6iG8tlOCvVJYiEnAW/lQ+BWvRUeWxY5CQAGPGmJ1EjlNZikhAyTvq5NttnqNgr+xhwf2VDgf076+itBifWUhdRKQhfL5hH2Vug3PbRJES38zsOCd74QXP9rLLzM0hp9HIUkQCimWPgl2zBkaPhvh4s5NIJTSyFJGAceBIMT/szAMstr/S4YBPPlFRWphGliISMBauzcFtQM+kGJJiLXIxha1boUkTmDDB7CRyBhpZikjAmL96DwDX9T7L5CTHPfsshIerKH2ARpYiEhB+3n+E9XsLsAfbrLG/svw8yrMsUtxyRipLEQkI83/cC0Bal5bENjP5RP8jR2DoUBg82NwcUmMqSxHxe2Vugw9Xe8ryut6J5oZxOCA2Fu6919wcUivaZykifu/77XnsKygmuqmdtK4tzAvywQeerYrS52hkKSJ+b/6PngN7ruqRQGiTYHNCvPsu3Hgj3HCDOe8v9aKyFBG/VugsZdH6fYCJU7BaFN3nqSxFxK8tWr+PY64yUuKb0SsppvEDFBVBq1bwhz80/ntLg1FZiohfm7MiC4Ab+iRis9ka980dDkhNVVH6AR3gIyJ+a+v+I6z85RDBQTZu7NPIU7DPP+/Zpqc37vuKV2hkKSJ+a07mbgAu7tqSllFhjffG69bB7bdDy5aN957iVRpZiohfKnaVMe/4UbC39E9uvDd2OOCjj1SUfkZlKSJ+6T8b9nG4yEWb6DAu7NxI51Zu3gxBQfDEE43zftJoVJYi4pfmrPBMwd7YN4ngoEY4sOe55yA6WkXpp7TPUkT8zq7cQr7fkYfNBjf1S/L+G5afR5lgoWtkSoNSWYqI35l9/HSRizq34KyYpt59s6NH4aKLPDfxWypLEfErx0rKmHv8KNhRA9t6980cDoiPh3vu8e77iOm0z1JE/MqHa/aSf8xFcmw4Q7p48YjUuXM9WxVlQNDIUkT8hmEYvPPdLgBuT23rvQN73nsPrr9ea70GEJWliPiNFTsPsnnfEZrag7mxj5cO7NGi6AHJZ6Zhp0+fTr9+/YiMjKRly5YMHz6cLVu2mB1LRCzkne93ATC811lEh9sb/g0KCz2LDUyc2PCvLZbmM2W5dOlSxo0bx/Lly8nIyKC0tJRLLrmEwsJCs6OJiAVkHz7GfzbsB2D0IC8c2ONwwIoVMHZsw7+2WJ7PTMN+/vnnJ3399ttv07JlS1atWsWFF15oUioRsYp/Lf+FMrfBwPaxdG0d1aCvHfTCC54/pKU16OuK7/CZsjxVfn4+ALGxsVU+xul04nQ6K74uKCgAwOVy4XK5vBuwFsqzWClTOatms2ousGa2E7NY7ecf6v+ZHXWW8q/lvwAwakBSg/33uVwuInfvxnnTTdiTksBCn5sVf87AurmgfplshmEYDZilURiGwTXXXMOhQ4f4+uuvq3zc5MmTmTJlymn3z549m/DwcG9GFLGU4uJiRowYAcCcOXMIC2vEK3A0giU5NhbsCqZFmMGEnmU01EGwnefOBZuNn2+6qWFeUExVVFTEyJEjyc/PJyqqdrMPPlmW48aN49NPP+Wbb74hMbHqa9RVNrJMSkoiJyeHuLi4xohaIy6Xi4yMDNLT07HbvXBQQj1YNZtVc4E1sxUWFtK8eXMADhw4QExMjLmBTlGfz8xV5uY3L35Ddn4xjqvP5paGWt5uwwaM+fNZ1KePpb6X5az4cwbWzQWQl5dHQkJCncrS56Zh77vvPj7++GOWLVt2xqIECA0NJTQ09LT77Xa75b6JYN1cYN1sVs0F1sp2Yg4r5TpVXbJ9tmEv2fnFxDUL4aZ+bbHbg+sf5C9/gVGjcD35JHz2md99Zo3Birnqk8dnytIwDO677z4WLFjAkiVLSElJMTuSiJjMMAzeWLoDgNGD2hHWEEVZfh5l69aW2kcp5vKZshw3bhyzZ8/mo48+IjIykn379gEQHR1N06ZeXihZRCzp2215bMwpoKk9uGHWgS0shMGDYejQ+r+W+BWfKcsZM2YAMGTIkJPuf/vtt7njjjsaP5CImG7G0m0A3NQ3kebN6rmijsPhWXBA51FKJXymLH3wOCQR8aJVvxzk2215NAmyMebC9vV7sffe82xVlFIFnylLEZETvfKFZ1R5Q59EEpvX41Sw99/XouhSLZWliPicNbsPs/TnXwkOsnHPkI51fyEtii41pLIUEZ/zf19sBeDaXmeRHFfHUeXRo7pws9SYzyykLiICsH5vPl9sPkCQDcal1XFU6XDAqlUqSqkxlaWI+JRXjo8qr+7RhpT4ZrV/gWef9WwvuqgBU4m/0zSsiPiMdXvyWbxxPzYb3Du0DqPKzZth1Cho06bhw4lf08hSRHzGc//ZDMA1PdrQsWVk7Z7scMAHH6gopU5UliLiE77blsvXW3OxB9sYn96ldk9etw5sNnjiCe+EE7+nshQRyzMMg2f/swWAkf2Ta3cE7PPPQ6tW8OSTXkongUD7LEXE8v6zYT9rdx8mPCSYe4d2qvkTy8+jbNnSO8EkYKgsRcTSSsvcPL/YM6q8c3AKLSJPv+xepY4dg9RUSE/3YjoJFCpLEbG0+T/uZduBo8SE22u+BqzD4bnE1u9/791wEjC0z1JELOuos5S/HB9VjhvSkaiwGly891//8mxVlNKANLIUEct67att/HrESdu4cG4fVIPrVc6bBzfdpLVepcFpZCkilrT7YBFvfbMTgD9ffjahTYLP/ASHAzZsUFGKV2hkKSKW9PRnmygpdXN+xzjSz2l15gcXFEBsLNx7b+OEk4CjkaWIWM7yHXksWr+PIBs8eeU52Gy2qh/scMBPP6koxatUliJiKWVuA8cnGwG4pX8yXVtHVf3gZ57xbAcPboRkEsg0DSsiljLr+11szCkgMqwJ49M7V/3AbdvgttsgMbHxwknA0shSRCxjf0Exzy/+GYBHL+tKXEQVCxBMnQrvv6+ilEajshQRy5i+6GeOOkvpkRTDyP7JlT9ozRrPdsKERsslorIUEUvYfNjGp8cP6nlqeDeCgio5qOevf/WMJrUoujQy7bMUEdMVu8r49w7Pv93vGJRCt7OiT39Q+aLo8fGNmEzEQ2UpIqZ7bckOcp02WkWFMv6SSg7qKS6Gfv1g2LDGDyeCylJETLZuTz5vfrMLgIlXdCUi9JRfSw4HtGkDd93V+OFEjtM+SxExTUmpm4c/WEuZ26BXnJtLTl2p5//9P89WRSkm08hSREzz6lfb2LzvCLHN7NyQcuzkv1ywAG6+GUJreP1KES/SyFJETLF+bz6vfbUNgMlXnk3EiVffcjhg3ToVpViGT5XlsmXLuOqqq2jTpg02m40PP/zQ7EgiUgee6defKHUbXH5ea4Z1a/2/v8zPh5gYmDjRtHwip/KpsiwsLKRHjx68+uqrZkcRkXp4+Yuf2ZRTQPNwO45rulXcH/TUU7BpE9x/v4npRE7nU/sshw0bxjAdOi7i05bvyOO1JdsBeOra84iPCMXlctFp3jxo3x4GDjQ5ocjpfKosa8vpdOJ0Oiu+LigoAMDlcuFyucyKdZryLFbKVM6q2ayaC6yZ7cQsZv785x9z8dDcNRgG3ND7LNK7xuNyuSj9+Wf2XHgh7UaOxG7Bz81K38tyVs1m1VxQv0w2wzCMBszSaGw2GwsWLGD48OFVPmby5MlMmTLltPtnz55NeHi4F9OJWEtxcTEjRowAYM6cOYSFhTV6BsOAd7YGsToviPgwg0e6lxEaDJ3nzsUICmLrjTc2eiYJLEVFRYwcOZL8/Hyios5w6bdK+HVZVjayTEpKIicnh7i4uEZIWTMul4uMjAzS09Ox2+3VP6ERWTWbVXOBNbMVFhbSvHlzAA4cOEBMTEyjZ5i/ei+Pzt9AkyAbc8b0p0diNPz4I0GLFuF85BHLfWZgze9lOatms2ougLy8PBISEupUln49DRsaGkpoJYee2+12y30Twbq5wLrZrJoLrJXtxBxm5Nrx61EcCzcD8FB6Z/qmxMOLL8Lo0TBgQMXUq5U+sxNZNRdYN5sVc9Unj1+XpYiY71hJGfe8+yOFJWX0T4ll7EUd/rcoemysueFEasinyvLo0aNs27at4uudO3eyZs0aYmNjSU6u4tp3ImKqiR+tZ/O+I8RHhPB/t/QiuMQJvXvDlVeaHU2kxnyqLFeuXElaWlrF1+PHjwdg9OjRzJw506RUIlKV9zN38+9VewiywSu39KLVS895rkf5u9+ZHU2kVnyqLIcMGYKPHo8kEnA2Zhfw5EfrAfjjJV0Y9PVCz1+oKMUH+VRZiohvKCh2cc+7q3CWuknr0oK7j2yCW27RWq/is3xquTsRsb4yt8GDc9awK6+Is2Ka8tfd/yVo7RoVpfg0laWINKjnF2/hy80HCG0SxIxrOtE8uhk8+aTZsUTqRdOwItJgPlqzlxnH1319Lmgb3Y/GwwMPmJxKpP40shSRBrF292Ee+eAnAO4O2c81TQ5Bv34mpxJpGBpZiki9HSgo5vezVuIsdXNx2wj+dMnZ0KG92bFEGoxGliJSL8WuMn4/axX7C5x0tB3jpUPLCVZRip/RyFJE6qzMbfDAnNWs2X2YaLuNt4K3EznhUbNjiTQ4laWI1Nm0Tzfynw37CcHg7zd1o915l5sdScQrNA0rInXyj2928va3uwB4IWQn/c9ra24gES/SyFJEam3RuhymfboRgMfburnq7vtMTiTiXRpZikitrPrlIA/OXYNhwKjmx/j9WF09RPyfylJEamzr/iPc9Y7nFJHfBB9m8sPXY7PZzI4l4nWahhWRGtl9sIhR/1jBoSIXPc6K4pU/XEpwkIpSAoNGliJSrV+POBn1jx/YV1BMJ9sxZv5uAOEh+re2BA79tIvIGeUfc3H7P1ewK6+IxCAXsx69kubNQsyOJdKoVJYiUqVjJWXc9U4mm3IKiA8L4l/3ptM6OszsWCKNTtOwIlKpklI3d7+7isxdh4iklFl/OJ928c3MjiViCo0sReQ0pWVuxr+/hiVbfiUs2MbbYy7g7IQos2OJmEYjSxE5SZnb4I//XsvCn3Kw4+b12/vSt12s2bFETKWyFJEKZW6Dh/+9lo/WZNMEg7+N6seQLi3NjiViOk3DiggAbrfBo/N+Yv7qvQTb4NVb+3DJua3NjiViCRpZighut8Hj89fxwao9BGPwyi29uaxbgtmxRCyj1iPLLVu28N577/H111+za9cuioqKaNGiBb169eLSSy/l+uuvJzQ01BtZRcQL3G6DP3+4nrkrdxOEwUu39OaK7ipKkRPVeGS5evVq0tPT6dGjB8uWLaNfv348+OCDTJ06ldtuuw3DMPjzn/9MmzZtePbZZ3E6nd7MLSINwDAMJn68nvdWZBGEwYsjenFVjzZmxxKxnBqPLIcPH87DDz/M3LlziY2t+si477//nhdffJEXXniBCRMmNEhIEWl4hmEw+eMN/Gt5FjYMnr+pJ9f0PMvsWCKWVOOy3Lp1KyEh1S9xlZqaSmpqKiUlJfUKJiLeYxgGjoUbeef7X7ABz93Qg+t6J5odS8SyajwNW5OiBCgqKqrV40WkcRmGwVOfbuLtb3cB8Oz13bmxb5K5oUQsrk5Hww4ZMoQ9e/acdv8PP/xAz54965vpjF577TVSUlIICwujT58+fP311159PxF/8+IX23jrm50APH3tedzUT0UpUp06nWcZFRVF9+7dee211xgxYgRutxuHw8H06dO57777Gjpjhblz5/Lggw/y2muvcf755/PGG28wbNgwNm7cSHJyco1fp7CwkLAw6ywG7XK5KC4uprCwELvdbnack1g1m1VzgTWzFRYWVvz5n0t/JsgexsSrzuGabnEn/Z1ZrPiZgXVzgXWzWTUXUL+fdaOOZsyYYTRr1sy45ZZbjNTUVOOss84yMjIy6vpyNdK/f39j7NixJ93XtWtX47HHHqv08cXFxUZ+fn7Fbffu3Qagm2666aZbAN/y8/Nr3T91LkvDMIzHHnvMsNlsht1uN7799tv6vFS1nE6nERwcbMyfP/+k+++//37jwgsvrPQ5kyZNMv2boptuuummm7VudSnLOk3DHjp0iLvuuosvvviCN954g6VLl3LJJZfw3HPPcc8999TlJauVm5tLWVkZrVq1Oun+Vq1asW/fvkqf8/jjjzN+/PiKrwsKCkhKSmL79u1nPP2lsblcLr788kuGDh1quWkLq2azai6wXrbXl+3g1YxN7H31NgB27txJTEyMuaFOYbXPrJxVc4F1s1k1F8DBgwfp0KFDnZ5bp7Ls1q0bKSkprF69mpSUFMaMGcPcuXO55557+PTTT/n000/rFKYmbDbbSV8bhnHafeVCQ0MrXU0oOjraUr8sXC4XYWFhxMTEWO6Hy6rZrJoLrJXtb19t4/Xvcgiy/28ffUxMjKV+/sFan9mJrJoLrJvNqrkAysrK6vzcOh0NO3bsWJYtW0ZKSkrFfTfffDNr16712vmV8fHxBAcHnzaKPHDgwGmjTRGBN5Zu5y//2QLAQ+mdTE4j4tvqVJZPPvkkQUGnPzUxMZGMjIx6h6pMSEgIffr0Oe31MzIyGDRokFfeU8RXvfX1DqYv2gzAH9M78/sL6zb1JCIeNS7LrKysWr3w3r17ax2mOuPHj+ett97in//8J5s2beKhhx4iKyuLsWPHNvh7ifiqmd/uZNqnmwC4/+JO3HexRpUi9VXjsuzXrx9jxoxhxYoVVT4mPz+fv//973Tr1o358+c3SMAT3Xzzzbz00ks4HA569uzJsmXL+Oyzz2jbtm2Dv5eIL5q1/Bcmf7IRgHFpHXjoNypKkYZQ4wN8Nm3axNNPP81ll12G3W6nb9++tGnThrCwMA4dOsTGjRvZsGEDffv25S9/+QvDhg3zSuB77rnHa0fciviy91Zk8eSH6wH4w4Xt+dMlXao8+E1EaqfGI8s9e/bw7LPPkp2dzeuvv07nzp3Jzc1l69atANx6662sWrWKb7/91mtFKSKVe3/lbibMXwfAnYNTeGxYVxWlSAOq8ciyV69e7Nu3jxYtWvDHP/6RzMxM4uLivJlNRGpg/o97ePSDtRjYuGNQO5644mwVpUgDq/HIMiYmhh07dgCwa9cu3G6310KJSM18sjabP/3bU5S3Dkhm0lXnqChFvKDGI8vrr7+eiy66iISEBGw2G3379iU4OLjSx5aXqoh4z5eb9/PQez/ixsaIfklMvaabilLES2pclm+++SbXXXcd27Zt4/7772fMmDFERkZ6M5uIVGH5jjzunrmCUoK4pmcbnrr2PIKCVJQi3lKr5e4uu+wyAFatWsUDDzygshQxwU97DnPXzBU4CeLiri15/sYeBKsoRbyqTmvDvv322w2dQ0Rq4Of9R7j91aUcpQmp7eP42629sQfXaSEuEakF/V8m4iOy8oq47bWvOUwTeiRG8/fRfQmzV37cgIg0LJWliA84UFDMrX9dzAGnQZdWkcz8bX8iQus0MSQidaCyFLG4I8Uu7pj+CbvL7CTHhjPrzv40bxZidiyRgKKyFLGwklI398xayUYjnPiIEGbd2Z+WUWHVP1FEGpTmcUQsyjAMHpv0L74uiyM8JJh/3tGPtnHNzI4lEpA0shSxqL9Mf4/5ZXEEB9n426296Z4YY3YkkYClshSxoFnvLOa1gmgApl93HmldWpqcSCSwaRpWxGK+mPQyk5wdABvj0ztzU98ksyOJBDyNLEUsZPP6ndxfklKx3ut9QzuaHUlE0MhSxDJyHc9wV1AvCo1gUtvHMXW4FkYXsQqVpYgFOB3TGFvciT3uUtrGhfOalrETsRT93yhiMiMnhz8nXMBKdwSRYU34x+h+WnRAxGI0shQxk8PBmyTyQVErgmzwt5G96dgywuxUInIKlaWIWb78km/KInm2pBUAE688hws7tzA5lIhURtOwImaYMYO9XXtwf5NuuA24sU8iowe1MzuViFRBI0uRxuZw4DRs3DN/EwcLSzi3TZSOfBWxOJWlSGMqKYFOnXCEdWPtD1lEN7Xz+m19dF1KEYtTWYo0lqlToUsXPuh8Ae/+ey02G7w0oidJseFmJxORamifpUhjeO01ALZcOIw/L1gHwAMXd9KaryI+QiNLEW9buhRuv51jIU2572/f4Cx1c1HnFtw/tJPZyUSkhnxmZPnUU08xaNAgwsPDiYmJMTuOSM04HJ6yjIhg2qcb+Xn/UVpEhvLCTT0ICtIBPSK+wmfKsqSkhBtvvJG7777b7CgiNZOdDaGhMHEii9bl8O4PWdhs8OJNPYmPCDU7nYjUgs9Mw06ZMgWAmTNnmhtEpAY6v/8+tG8Pjz7K3sPHeHTeTwD84cIODO4Ub3I6EaktnynLunA6nTidzoqvCwoKAHC5XLhcLrNinaY8i5UylbNqNqvmAjCmTgXDwNWhA2XOEh5470cKikvpnhjF/WkppmQ+8T2t9vMP1v1+WjUXWDebVXNB/TLZDMMwGjCL182cOZMHH3yQw4cPV/vYyZMnV4xITzR79mzCw3W4vjS8kMOHCT18mCPt2gHwxV4bH2cFExpk8EiPMuLDzMlVXFzMiBEjAJgzZw5hYSYFETFRUVERI0eOJD8/n6ioqFo919SRZVVldqLMzEz69u1bp9d//PHHGT9+fMXXBQUFJCUlkZaWRlxcXJ1e0xtcLhcZGRmkp6djt9vNjnMSq2azYq6gadMgPBznffeRkZFBux6DWLQiEzCYdPW53Ngn0bRshYWFFX8eOnSo5Q6Ss+L3E6ybC6ybzaq5APLy8ur8XFPL8t577634125V2h3/F3pdhIaGEhp6+oEUdrvdct9EsG4usG42y+TKyIDgYHj0UewuF2Vu+PPHm3GVGaR1acEtA9qZupzdiZ+RZT6zSlg1m1VzgXWzWTFXffKYWpbx8fHEx+tgB/Fxb74Jo0ZBenrFXRl7bazPLiC6qZ1nru+udV9FfJzPHOCTlZXFwYMHycrKoqysjDVr1gDQsWNHIiJ0/T8xydSpnm3TphV3bcgu4D97PWdlOa45l1ZR2j8o4ut8piwnTpzIO++8U/F1r169APjqq68YMmSISakkoJWUeE4PufXWirtcZW4em78et2HjknNacnWPNiYGFJGG4jOLEsycORPDME67qSjFFA4HfPLJSUUJ8Pevd7B5/1GaNTFwXHW2pl9F/ITPlKWIZbz6qmd7/fUn3f1LXiEv/3crAMPbuYnTKj0ifsNnpmFFLOGbb+D22+GUc7QMw+CJD9fjLHUzqH0s/eIPmBRQRLxBI0uRmnI44MsvTytKgA/X7OXrrbmENgnCcfU5aPZVxL+oLEVqYs8eCAmBiRNP+6tDhSVMXbgJgPsv7kTbOK0OJeJvVJYi1XnqKTh2DB57rNK/fn7xFg4WltClVSRjLmjfyOFEpDGoLEXOZOpUKCuDTpVfqHn93nxmr8gCPOdUhjTR/1Ii/kgH+IhUJTcXrroKevas9K8Nw2DKJxswDLiqRxsGtLfOesMi0rBUliKVmToVmjWDExbiP9XHa7PJ3HWIpvZgHh/WtRHDiUhj05yRyKk+/9yzPUNRFjpLefozz0E949I60CamaZWPFRHfp5GlyIneegtuuw0uu+yMD3v1q23sL3CSHBvOXTqoR8TvqSxFyjkcnm01F0bee/gY//hmJwBPXHE2YfZgbycTEZOpLEUAnE5o186zOk81Xli8hZJSNwNSYkk/p5X3s4mI6VSWIg4HnHdejYpyY3YBC1bvBeDxy7VQukig0AE+EtheecWzvfbaGj38mc83YxhwRfcEeibFeC+XiFiKRpYSuL7/HkaPhujoGj38m625LPv5V+zBNh65tIuXw4mIlagsJTCVH8yTmlqjh7vdBtMXeU4VuXVAW9rGNfNWMhGxIJWlBJ6sLLDb4fHHa/yUT9flsCG7gIjQJtw3tKMXw4mIFWmfpQSW6dOhtLRWRVnmNnj5C89Fne+6IEUXdRYJQBpZSuCYOtWzbV+7RQQW/pTNtgNHiQprwu8Gp3ghmIhYncpSAsPBg3DFFdC7d62eduKo8vcXticqzO6NdCJicSpL8X8OB0RGwkMP1fqpH6/dy45fC4kJtzN6ULuGzyYiPkH7LMW/LVzo2dahKEvL3LzyxTYAxlzQnkiNKkUClkaW4r/++U8YORKuvLJOT/9oTTY7cwuJbRaiUaVIgFNZin+q4aLoVSlzG/ztK8+o8vcXticiVP+riAQy/QYQ/+N0QnIy3HFHnV8iY+M+duQWEt3Uzm0D2zZcNhHxSSpL8S8OB/TsWa+iNAyDGUu2A3B7aluNKkVEB/iIH3n5Zc/26qvr9TLf78hj7Z58wuxB3KF9lSKCj5Tlrl27uPPOO0lJSaFp06Z06NCBSZMmUVJSYnY0sYrMTM+i6BMn1vulykeVN/VN0mo9IgL4yDTs5s2bcbvdvPHGG3Ts2JH169czZswYCgsLef75582OJ2YrX5mnX796v9T6vfl8vTWX4CAbYy6o3Uo/IuK/fKIsL7vsMi677LKKr9u3b8+WLVuYMWOGyjLQ7doFTZrUaq3XM3l9qWdUeWX3BJJiwxvkNUXE9/lEWVYmPz+f2NjYMz7G6XTidDorvi4oKADA5XLhcrm8mq82yrNYKVM5q2ZzuVx0+uADSidMgD/9CRogX9bBIj5blwPAnYPa1vm/2Yqf2YlZrPbzD9b8zMC6ucC62ayaC+qXyWYYhtGAWRrF9u3b6d27Ny+88AJ33XVXlY+bPHkyU6ZMOe3+2bNnEx6uUYMv6zx3LgA/33xzg73mgl1BLMkJomu0m7vPcTfY61pBcXExI0aMAGDOnDmE1fH8UxFfVlRUxMiRI8nPzycqKqpWzzW1LKsqsxNlZmbSt2/fiq+zs7O56KKLuOiii3jrrbfO+NzKRpZJSUnk5OQQFxdXv/ANyOVykZGRQXp6Ona7tZZUs2S2w4cp27SJ/xw61GC5jjpLueAvyzjqLOWtUb24qHOLOr+WFT+zwsJCmjdvDsCBAweIiYkxN9AprPiZgXVzgXWzWTUXQF5eHgkJCXUqS1OnYe+9996Kf+1WpV27dhV/zs7OJi0tjdTUVN58881qXz80NJTQ0NOPZrTb7Zb7JoJ1c4GFsjkcEB0N99wDn33WYLk+ztzLUWcp7eObMfTsBIKCbPV+Tct8ZnBSDivlOpVVs1k1F1g3mxVz1SePqWUZHx9PfHx8jR67d+9e0tLS6NOnD2+//TZBQT5x1os0pI8/9mwfeKBB9lGWc7sNZn63C4A7zm/XIEUpIv7FJw7wyc7OZsiQISQnJ/P888/z66+/Vvxd69atTUwmjWbmTLjllnovOFCZpVt/ZWduIZGhTbiud2KDv76I+D6fKMvFixezbds2tm3bRmLiyb/MfPD4JKmt8kXRK5lSbwhvf7sLgJv6JWlpOxGplE/MZd5xxx0YhlHpTfxccTEkJjbIyjyV2XbgKMt+/hWbDUantvPKe4iI79M/o8W6pk6F3r3hd7/z2lvM/iELgIu7tiQ5TqcTiUjlfGJkKQHopZc82yuu8NpbFLvKmPfjHgBuHaDLcIlI1TSyFOv58Ue4/XaoZoWm+vpsXQ75x1ycFdOUC+txXqWI+D+NLMVaHA5YuNDrRQn/m4Id0S+JYJ0uIiJnoJGlWMf27Z5F0SdM8Ppb/bz/CCt/OURwkI2b+iV5/f1ExLdpZCnWMH062O2NUpTwv1Hlb85uSasorZMqImemkaWYr/w8yuTkRnm7YyX/O7BnpA7sEZEaUFmKufLzIT0dUlMb7S0/W5fDkeJSkmKbckHHmi23KCKBTWUp5nE4ICYG7r+/Ud/2g1WeUeVNfZK0DqyI1Ij2WYo5FizwbBu5KHcfLOL7HXnYbHBdH60DKyI1o5GlNL5Zs+Dmm+Haaxv9rRes3gvAoA5xnBXTtNHfX0R8k8pSGtfUqZ5tSEijv7VhGBVTsDdoVCkitaCylMZTXAwJCXDXXaa8feauQ2QdLKJZSDCXnqtLu4lIzakspXE4HNC/v2lFCfDBqt0AXNE9gfAQ/eiLSM3pAB/xvhde8Gwvu8y0CEUlpXy2bh8AN/TRij0iUjv657V415o1MHo0xJt7PuPiDfs56iwlOTacfu2am5pFRHyPRpbiPQ4HfPKJ6UUJ8NEaz1Gw1/Y6C5tN51aKSO1oZCnesXUrBAfDn/9sdhIOFZbw9dZcAK7u2cbkNCLiizSylIb3zDPQtKklihLgs/U5lLoNzm0TRYcWEWbHEREfpJGlNKzyRdETrXMe48drsgG4uodGlSJSNypLaThHjsDQoTB4sNlJKuzLL2bFroMAXKmyFJE6UllKw5g6FWJjYdw4s5OcZOFP2RgG9GvXXMvbiUidaZ+l1N+8eZ6txYoS4JO1ninYqzSqFJF60MhS6ufdd+HGG+H6681OcppduYWs3ZNPcJCNy89LMDuOiPgwlaXUXfnBPCYsil4TC3/yjCoHdYgjPiLU5DQi4stUllI3RUXQqhX84Q9mJ6nSovWe5e2u7K5RpYjUj8pSas/hgNRUSxfl7oNFbMguIMgG6efoCiMiUj86wEdq5/nnPdv0dHNzVOPz46PKASlxxDaz5jSxiPgOnynLq6++muTkZMLCwkhISGDUqFFkZ2ebHSuwrFsHt98OEyeanaRan2/wlOWw8zSqFJH685myTEtL4/3332fLli3MmzeP7du3c8MNN5gdK2AETZsGH34ILVuaHaVaBwqKWfXLIQAu0RSsiDQAn9ln+dBDD1X8uW3btjz22GMMHz4cl8uF3W43MZn/i9izB4KC4MknzY5SI/85PqrslRxD6+gwk9OIiD/wmbI80cGDB3n33XcZNGjQGYvS6XTidDorvi4oKADA5XLhcrm8nrOmyrNYKVM549lncZ11Fs6HH8ZuoXxn+swWrcsBIP3sFqZ8plb8fp6YxWo//2DNzwysmwusm82quaB+mWyGYRgNmMWrHn30UV599VWKiooYOHAgCxcuJC4ursrHT548mSlTppx2/+zZswkPD/dmVL/Qee5cAH6++WaTk9RcoQueWBmMGxtP9iolXgNLAIqLixkxYgQAc+bMISxMH4wEnqKiIkaOHEl+fj5RUVG1eq6pZVlVmZ0oMzOTvn37ApCbm8vBgwf55ZdfmDJlCtHR0SxcuLDKi/lWNrJMSkoiJyfnjCXb2FwuFxkZGaSnp1tnSvnoUWw//khJaqr1slH1Z/bBj3t5fMEGuraO5JNxqZbKZqbCwkKaN28OwIEDB4iJiTE30Cms+JmBdXOBdbNZNRdAXl4eCQkJdSpLU6dh77333op/7ValXbt2FX+Oj48nPj6ezp07c/bZZ5OUlMTy5ctJTa38l2JoaCihoaev3GK32y33TQQL5XI4ID4e7rkH4/i0hWWyneLUXF9s9lzk+bJurU3Pa6XP7MQcVsp1Kqtms2ousG42K+aqTx5Ty7K8/OqifEB84shRGsDxqVfuucfcHHVQ7Crj222eskw/p5XJaUTEn/jEAT4rVqxgxYoVDB48mObNm7Njxw4mTpxIhw4dqhxVSh28955nQXSLrvVane935HHMVUbrqDDOSajdFIuIyJn4RFk2bdqU+fPnM2nSJAoLC0lISOCyyy5jzpw5lU6zSh1YfFH0mvhi034Ahp7dssr92CIideETZXneeefx5Zdfmh3DfxUWQosWcPfdZiepM8Mw+HLTAQB+c7b1F04QEd/iMyv4iJc4HPDDDz5dlACbco6QnV9MmD2IQR3qth9cRKQqKstA9pe/eLZDh5qbowF8udkzBXt+h3jC7MEmpxERf+MT07DiBRs3wqhR0No/1k79YrNnCvbis3UUrIg0PI0sA9HUqTB/vt8UZe5RJ2t2HwZgaFftrxSRhqeyDDQbN4LNBk88YXaSBvPV5gMYBpzbJkoLp4uIV6gsA8lf/gKxsX5VlABfbTk+BatRpYh4ifZZBory8yj9ZOq1XGmZm6+3elbtGaKyFBEvUVkGgsJCGDzYL456PdW6vQUcKS4lKqwJPRJjzI4jIn5KZenvHA6fX3DgTL4+vhbs4E7xBAdp1R4R8Q7ts/Rn773n2fppUQJ8vS0PgAs7tTA5iYj4M40s/dXcuT69KHpNFJXCT3vyAbiws8pSRLxHZemP/GBR9Jr4Od+G24COLSNoE9PU7Dgi4sdUlv7m6NGKCzf7u82HPfsoL+iktWBFxLu0z9KfTJ0Kq1YFRFEahlFRlpqCFRFvU1n6i+ee82wvusjcHI1kR24Rh0ps2INtDEyJMzuOiPg5TcP6g82bPYuiJySYnaTRlJ8y0q9tc5qG6CojIuJdGln6OocDPvggoIoS4Jvjp4wM7qRRpYh4n8rSl61b53eLoteEq8zNyl2HABjUXmUpIt6nsvRVzz8PrVrBk0+anaTR/bQnn8KSMsKbGJzdOtLsOCISALTP0heVn0fZMjAXDl++wzMF2zHKIEhL3IlII1BZ+pqiIkhNhfR0s5OY5vvtnrLsFGWYnEREAoXK0pc4HJ5LbP3+92YnMY2ztIzMXQcB6BStshSRxqF9lr7i3Xc92wAuSoA1WYdxlrqJaxZCa61wJyKNRCNLXzBvHtx4o9+v9VoT3x2fgh2YEovNVmRyGhEJFBpZWt3UqbBxo4ryuO+PH9wzsH2syUlEJJCoLK3syBGIjQ3I00Mqc6ykjDVZhwEY2L65uWFEJKCoLK3K4YC1a2HcOLOTWMaqXw5RUuYmITqMtrHhZscRkQCisrSiZ57xbAcPNjeHxXy/w7MebGr7OGw2nV8pIo3H58rS6XTSs2dPbDYba9asMTtOw9u6FW67DSZONDuJ5ZSfX5naQUvciUjj8rmyfOSRR2jTpo3ZMbwiaNo0eP99SEw0O4rlHCsp46c9+QAM1HqwItLIfOrUkUWLFrF48WLmzZvHokWLqn280+nE6XRWfF1QUACAy+XC5XJ5LWdtuVwuonbsoMwwcD/yCFgs24lbs6zceZBSt0GrqFBaRTSxTK7KWDHbiVms9vMP1vzMwLq5wLrZrJoL6pfJZhiGTyyDsn//fvr06cOHH35IfHw8KSkprF69mp49e1b5nMmTJzNlypTT7p89ezbh4dY5QKTDhx+ye+hQSqKizI5iWf/ZY+Oz3cH0inNzR2e32XF8TnFxMSNGjABgzpw5hIWFmZxIpPEVFRUxcuRI8vPziarl71ufKEvDMLj88ss5//zzeeKJJ9i1a1eNyrKykWVSUhI5OTnExVljKi9o2jTK3G4W9e1Leno6drvd7EgncblcZGRkmJ7tjpmr+HZ7HpOu7MptA5Itk6syVsxWWFhI8+ae020OHDhATEyMuYFOYcXPDKybC6ybzaq5APLy8khISKhTWZo6DVvVyO9EmZmZfPfddxQUFPD444/X6vVDQ0MJDQ097X673W6Nb2JxMaSm4r74YvjsM+vkqoSZ2UrL3KzZfRiAgR1anJRDn1nN6DOrH6vmAutms2Ku+uQxtSzvvffeiqmhqrRr145p06axfPny04qvb9++3HrrrbzzzjvejOkdU6dCQgLcdZel9lFa0aacIxSWlBEZ1oTOrXT9ShFpfKaWZXx8PPHx8dU+7pVXXmHatGkVX2dnZ3PppZcyd+5cBgwY4M2I3jFrlmd7113m5vARK45fZaRv2+YE6/qVImICnzgaNjk5+aSvIyIiAOjQoQOJvnaaxYIFcPPNWuu1FlYeL8t+KVoPVkTM4XPnWfo0hwPWrVNR1oJhGBXXr+zXTmUpIubwiZHlqdq1a4cPHMR7svx8iImB++83O4lP2ZVXRO7REkKaBNE9MdrsOCISoDSybAwOh+cyWyrKWsvc6RlV9kiMJrRJsMlpRCRQqSy9bfp0zzY11dwcPmqFpmBFxAJ8chrWZ2zfDrfeCqccoCQ1p4N7RMQKNLL0FocD5s5VUdZD3lEnu/KKAOidpIs9i4h5VJbesGoV2GwwYYLZSXxa+ao9HVtGEB1urZVARCSwqCwb2ksvQUoKPPmk2Ul83uqswwD0SooxNYeIiPZZNqSpUz3bWO1fawirdx8CoFeypmBFxFwqy4ZSXAy9e8MVV5idxC+UuQ3W7vZc7LlXcoy5YUQk4KksG4LDAYmJ8LvfmZ3Eb2w7cJSjzlLCQ4K1eLqImE77LOtr5kzPVkXZoFZneaZgeyTGaPF0ETGdRpb18fHHcMstUMk1M6V+Kg7u0RSsiFiARpZ15XDAmjUqSi/RwT0iYiUaWdbF4cMQHQ0PPGB2Er9UUOxi64GjAPTUaSMiYgEaWdaWwwE//6yi9KKfdudjGJAU25QWkRq5i4j5VJa1Ub4oev/+5ubwc+UH9/TSEnciYhGahq2pXbs8B/O0a2d2Er+3+vgydzq4R0SsQiPLmpg6Fd57T0XZCAzD+N/IUgf3iIhFqCyrk5np2T7+uLk5AsSeQ8c4VOTCHmzj7AQtRiAi1qBp2DN5+WUYPRr69TM7ScD4aY9nibuuraMIbRJschoREQ+VZVUcDs82JsbUGIHmp72HATgvMdrcICIiJ1BZVsbphJ494eqrzU4ScNbv9Ywsu5+lshQR61BZnsrhgORkuOMOs5MEHMMwKqZhNbIUESvRAT4n+uc/PVsVpSl+ySviSHEpIU2CdKUREbEUjSzLLVwII0dCWJjZSQLWT8enYM9JiMIerH/HiYh16DcSeKZef/xRRWmydXsOA3Ce9leKiMVoZHnwIERFwYMPmp0k4Gl/pYhYVWCPLKdO9Sxjp6I0ndttsCG7AIDuKksRsRifKct27dphs9lOuj322GN1f8HyRdF7926YgFIvO/MKOeosJcweRMcWEWbHERE5iU9NwzocDsaMGVPxdUREHX+p7t4NN98M7ds3UDKpr3XHp2DPbRNNEx3cIyIW41O/lSIjI2ndunXFra5lGfTBBypKi6nYX6mDe0TEgnxqZPnss88ydepUkpKSuPHGG3n44YcJCQmp8vFOpxOn01nxdX6+5xdy7ujRuPPyvJ63plwuF0VFReTl5WG3282Oc5LGyrZq6x7cziLaRRjk1eB7o8+sdgoLCyv+fPDgQcrKykxMczorfmZg3Vxg3WxWzQWen33wLIBSa4aP+Otf/2osWbLEWLt2rfH3v//diI+PN+68884zPmfSpEkGoJtuuummm24Vt+3bt9e6g2yGUZeKbRiTJ09mypQpZ3xMZmYmffv2Pe3+efPmccMNN5Cbm0tcXFylzz11ZHn48GHatm1LVlYW0dHR9QvfgAoKCkhKSmL37t1ERUWZHeckVs1m1Vxg3WxWzQXWzWbVXGDdbFbNBZ7ZxeTkZA4dOkRMLS+SYeo07L333suIESPO+Jh2VVxweeDAgQBs27atyrIMDQ0lNDT0tPujo6Mt900EiIqKsmQusG42q+YC62azai6wbjar5gLrZrNqLoCgoNofrmNqWcbHxxMfH1+n565evRqAhISEhowkIiJyGp84wOf7779n+fLlpKWlER0dTWZmJg899BBXX301ycnJZscTERE/5xNlGRoayty5c5kyZQpOp5O2bdsyZswYHnnkkVq/zqRJkyqdmjWTVXOBdbNZNRdYN5tVc4F1s1k1F1g3m1VzQf2ymXqAj4iIiC/wqUUJREREzKCyFBERqYbKUkREpBoqSxERkWoEbFk2+CW/vMDpdNKzZ09sNhtr1qwxO07FqTphYWEkJCQwatQosrOzzY7Frl27uPPOO0lJSaFp06Z06NCBSZMmUVJSYnY0nnrqKQYNGkR4eHitVwxpaK+99hopKSmEhYXRp08fvv76a1PzACxbtoyrrrqKNm3aYLPZ+PDDD82OBMD06dPp168fkZGRtGzZkuHDh7NlyxazYzFjxgy6d+9eccJ/amoqixYtMjtWpaZPn47NZuNBk68XPHny5NN+17du3brWrxOwZQmeS37l5ORU3J544gmzI53kkUceoU2bNmbHqJCWlsb777/Pli1bmDdvHtu3b+eGG24wOxabN2/G7XbzxhtvsGHDBl588UVef/11JkyYYHY0SkpKuPHGG7n77rtNzTF37lwefPBB/vznP7N69WouuOAChg0bRlZWlqm5CgsL6dGjB6+++qqpOU61dOlSxo0bx/Lly8nIyKC0tJRLLrnkpAXpzZCYmMgzzzzDypUrWblyJUOHDuWaa65hw4YNpuY6VWZmJm+++Sbdu3c3OwoA55577km/69etW1f7F6nLoub+oG3btsaLL75odowqffbZZ0bXrl2NDRs2GICxevVqsyOd5qOPPjJsNptRUlJidpTTPPfcc0ZKSorZMSq8/fbbRnR0tGnv379/f2Ps2LEn3de1a1fjscceMynR6QBjwYIFZseo1IEDBwzAWLp0qdlRTtO8eXPjrbfeMjtGhSNHjhidOnUyMjIyjIsuush44IEHTM0zadIko0ePHvV+nYAeWT777LPExcXRs2dPnnrqKUtM2wHs37+fMWPGMGvWLMLDw82OU6mDBw/y7rvvMmjQIMtdhgc8CybHxsaaHcMSSkpKWLVqFZdccslJ919yySV89913JqXyLeWX97PSz1RZWRlz5syhsLCQ1NRUs+NUGDduHFdccQW/+c1vzI5SYevWrbRp04aUlBRGjBjBjh07av0aPrGCjzc88MAD9O7dm+bNm7NixQoef/xxdu7cyVtvvWVqLsMwuOOOOxg7dix9+/Zl165dpuY51aOPPsqrr75KUVERAwcOZOHChWZHOs327dv5v//7P1544QWzo1hCbm4uZWVltGrV6qT7W7Vqxb59+0xK5TsMw2D8+PEMHjyYbt26mR2HdevWkZqaSnFxMRERESxYsIBzzjnH7FgAzJkzhx9//JHMzEyzo1QYMGAA/+///T86d+7M/v37mTZtGoMGDWLDhg1VXoSjUvUem1pITa5fmZmZWelzP/jgAwMwcnNzTc328ssvG4MGDTJKS0sNwzCMnTt3enUatraf2a+//mps2bLFWLx4sXH++ecbl19+ueF2uy2RzTAMY+/evUbHjh2rvdZpY+cycxp27969BmB89913J90/bdo0o0uXLqZkqgwWnYa95557jLZt2xq7d+82O4phGIbhdDqNrVu3GpmZmcZjjz1mxMfHGxs2bDA7lpGVlWW0bNnSWLNmTcV9VpiGPdXRo0eNVq1aGS+88EKtnudXy93l5uaSm5t7xse0a9eOsLCw0+7fu3cviYmJLF++nAEDBpiWbcSIEXzyySfYbLaK+8vKyggODubWW2/lnXfeMSVXZZ/Znj17SEpK4rvvvvPKNFBts2VnZ5OWlsaAAQOYOXNmnS7D441cADNnzuTBBx/k8OHDXsl0JiUlJYSHh/Pvf/+ba6+9tuL+Bx54gDVr1rB06dJGz1QZm83GggULGD58uNlRKtx33318+OGHLFu2jJSUFLPjVOo3v/kNHTp04I033jA1x4cffsi1115LcHBwxX1lZWXYbDaCgoJwOp0n/Z2Z0tPT6dixIzNmzKjxc/xqGtbKl/yqabZXXnmFadOmVXydnZ3NpZdeyty5c71S4vX5zMr/nXXiBbYbUm2y7d27l7S0NPr06cPbb7/ttaKsbS4rCAkJoU+fPmRkZJxUlhkZGVxzzTUmJrMuwzC47777WLBgAUuWLLFsUYInq7f+H6yNiy+++LSjTH/729/StWtXHn30UcsUpdPpZNOmTVxwwQW1ep5flWVNWfmSX6e+f0REBAAdOnQgMTHRjEgArFixghUrVjB48GCaN2/Ojh07mDhxIh06dDD94ILs7GyGDBlCcnIyzz//PL/++mvF39XlfKqGlJWVxcGDB8nKyqKsrKzifNmOHTtWfG8bw/jx4xk1ahR9+/YlNTWVN998k6ysLMaOHdtoGSpz9OhRtm3bVvH1zp07WbNmDbGxsab+vzhu3Dhmz57NRx99RGRkZMW+3ejoaJo2bWpargkTJjBs2DCSkpI4cuQIc+bMYcmSJXz++eemZSoXGRl52j7dZs2aERcXZ+q+3j/96U9cddVVJCcnc+DAAaZNm0ZBQQGjR4+u3Qs1/Iyw9a1atcoYMGCAER0dbYSFhRldunQxJk2aZBQWFpod7TTe3mdZUz/99JORlpZmxMbGGqGhoUa7du2MsWPHGnv27DE1l2F49gdSxb5Ds40ePbrSXF999VWjZ/nb3/5mtG3b1ggJCTF69+5tidMgvvrqq0o/n9GjR5uaq6qfp7ffftvUXL/73e8qvoctWrQwLr74YmPx4sWmZjoTK+yzvPnmm42EhATDbrcbbdq0Ma677ro67eP1q32WIiIi3hDQ51mKiIjUhMpSRESkGipLERGRaqgsRUREqqGyFBERqYbKUkREpBoqSxERkWqoLEVERKqhshQREamGylJERKQaKksREZFqqCxF/Nyvv/5K69atefrppyvu++GHHwgJCWHx4sUmJhPxHVpIXSQAfPbZZwwfPpzvvvuOrl270qtXL6644gpeeukls6OJ+ASVpUiAGDduHP/973/p168fa9euJTMzk7CwMLNjifgElaVIgDh27BjdunVj9+7drFy5ku7du5sdScRnaJ+lSIDYsWMH2dnZuN1ufvnlF7PjiPgUjSxFAkBJSQn9+/enZ8+edO3alb/+9a+sW7eOVq1amR1NxCeoLEUCwMMPP8wHH3zA2rVriYiIIC0tjcjISBYuXGh2NBGfoGlYET+3ZMkSXnrpJWbNmkVUVBRBQUHMmjWLb775hhkzZpgdT8QnaGQpIiJSDY0sRUREqqGyFBERqYbKUkREpBoqSxERkWqoLEVERKqhshQREamGylJERKQaKksREZFqqCxFRESqobIUERGphspSRESkGv8fQhB8W8wNSyYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 双曲正弦函数\n",
    "f_array = np.sinh(x_array)\n",
    "visualize_fx(x_array, f_array, '双曲正弦函数')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "158cfec7-ef60-499d-b240-2926571a4224",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 双曲余弦函数\n",
    "f_array = np.cosh(x_array)\n",
    "visualize_fx(x_array, f_array, '双曲余弦函数')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "73c6daa1-1820-4d5b-a75e-6270b0f11bed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 双曲正切函数\n",
    "f_array = np.tanh(x_array)\n",
    "visualize_fx(x_array, f_array, '双曲正切函数')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9ab22753-4a02-4239-95f4-743af49707a2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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R0dHRhovsd/A7yNpg93ri9nOKOT/BdX+FG1NQUMCIESPIzc0lNja2Vvd15bAcO3Ysb7zxBu+99x4dOnSo8naVrSxTUlLYu3cviYmJjZFaI4FAgOzsbDIyMoiKijKdU46tbbZ2gZ1t+fn5tGnTBoADBw4QHx9vNugkNj5mX3+wgUFvHqB5E4c5I3rQrJldg7NVlIddG9cwaJA9jxnY+VyWOnz4MMnJyXUalnY9+zVw11138fe//53Vq1efclACeL1evF5vheujoqKsexLB3i6wt83WLrCr7cQOm7pOZk3bo4/S7Oc3AAdo6oH+57Szo+sEgUCA3Z9Z9JidxMau+vS4Zlg6jsNdd93F0qVLWblyJampqaaTRCQclb6PMinJbIdYxTXDcuzYsSxcuJDXXnuN1q1bs2/fPgDi4uJo0aKF4ToRCQv5+dCvHwwcCAePm64Ri7hmWM6dOxeAAQMGlLt+/vz53HrrrY0fJCLhxecLnnBA76OUSrhmWLrwOCQRcYsXXwxuNSilCq4ZliIiIfHSSzopulRLw1JEIpdOii41pGEpIpHp+HF9cLPUmGtOpC4i0mB8Pli3ToNSakzDUkQiy8MPB7f9+5vtEFfRy7AiEjm+/BJGjoT27U2XiMtoZSkikcHng5df1qCUOtGwFJHwt3EjeDzwwAOmS8SlNCxFJLzNmgXt2sHvfme6RFxM+yxFJHyVvo+ybVuzHeJ6GpYiEp6++w7S0iAjw3SJhAENSxEJPz4fnH46/Pd/my6RMKF9liISXv7v/4JbDUppQFpZikj4WLIEfvELnetVGpxWliISHnw+2LRJg1JCQitLEXG/vDxISIA77zRdImFKK0sRcTefDz79VINSQkrDUkTc66GHgtt+/cx2SNjTy7Ai4k5bt8LNN0OHDqZLJAJoZSki7pOZCS+9pEEpjUbDUkTcZcOG4HbyZKMZElk0LEXEPX7/++BqUidFl0amfZYi4g6lJ0VPSjLbIRFJw1JE7FdYCH36wJAhpkskQmlYiojdfD5o3x5uv910iUQw7bMUEXv99a/BrQalGKaVpYjYaelSGDYMvF7TJSJaWYqIhXw+2LhRg1Ks4aphuXr1aq688krat2+Px+Ph1VdfNZ0kIg0tNxfi42HKFNMlImVcNSzz8/O54IILeOqpp0yniEgINJkxA774Au6+23SKSDmu2mc5ZMgQhujQcZGwUhgo5t1/H+TAG2v4f+1Op0mrTvDZXtNZ7M/zm04Qi7hqWNaW3+/H7//PL3xeXh4AgUCAQCBgKquC0habmkrZ2mZrF9jZdmKLbb//j761mT//6xtI6AcB4P8+Np1UThOPXc9lKRt/z8DeLqhfU1gPy5kzZzJ9+vQK17/zzjvExMQYKDq17Oxs0wlVsrXN1i6wq62wsLDs67fffpvo6GiDNeVt+8cuaNmZBK9DXHPTNRX1Siqx6rk8ma1tNnYVFBTU+b5hPSwnTZrEhAkTyr7Py8sjJSWF9PR0EhMTDZaVFwgEyM7OJiMjg6ioKNM55djaZmsX2NmWn59f9vXAgQOJj483F3Oijz/mH61zoQT6J5cw45bLrHnMwM7nspStbbZ2ARw+fLjO9w3rYen1evFWcuh5VFSUdU8i2NsF9rbZ2gV2tZ3YYU3X44/DqFF4zm8On+wBLGo7ia1dYG+bjV316XHV0bAiEiZ8Pjh2DBISTJeI1IirVpbHjx9n69atZd9//fXXbNiwgYSEBDp27GiwTERqrLAQevaEn//cdIlIjblqWH700Uekp6eXfV+6P3LUqFEsWLDAUJWI1JjPF/w8yl/9ynSJSK24algOGDAAx3FMZ4hIXZT+g1aDUlzIVcNSRFzq9dfhxht1rldxLR3gIyKhlZkJGzZoUIqraWUpIqFz9CjExsK4caZLROpFK0sRCQ2fD7Zs0aCUsKBhKSIN78EHg9s+fcx2iDQQvQwrIg1r+/bgwTypqaZLRBqMVpYi0nB8PnjxRQ1KCTsaliLSMNauDW4nTTLbIRICehlWROrviSdg1Ci46CLTJSIhoWEpIvXj8wW3tnzsl0gIaFiKSN35/dCjB1x1lekSkZDSsBSRusnMhI4dgy+/ioQ5HeAjIrX3l78EtxqUEiG0shSR2nnjDRgxAqKjTZeINBqtLEWk5nw+WLdOg1IijlaWIlIzhw9D69Zwzz2mS0QanVaWIlI9nw+++UaDUiKWhqWInFrpSdF79jTbIWKQXoYVkart2AHDhkGXLqZLRIzSylJEKufzwQsvaFCKoGEpIpX54IPgVidFFwH0MqyInOwPf4BbboG0NNMlItbQsBSR/8jMDG7j4sx2iFim1sNy8+bNvPjii7z77rts376dgoICTjvtNC688EIuv/xyrrvuOrxebyhaRSSUioqgWze45hrTJSLWqfE+y/Xr15ORkcEFF1zA6tWr6dOnD+PHjyczM5Obb74Zx3H47W9/S/v27Xn44Yfx+/2h7BaRhuTzweLFGpQiVajxynLo0KHce++9LF68mISEhCpv98EHH/D444/z2GOPMXny5AaJFJEQeuaZ4HbkSLMdIhar8bDcsmULzZs3r/Z2aWlppKWlUVRUVK8wEWkEb70FN98MLVqYLhGxWo1fhq3JoAQoKCio1e1FxBCfD9au1aAUqYE6vc9ywIAB7Nq1q8L1H374IT169Khv0ynNmTOH1NRUoqOj6dWrF++++25I/zyRsHToELRsCVOmmC4RcYU6vXUkNjaW7t27M2fOHIYPH05JSQk+n4+ZM2dy1113NXRjmcWLFzN+/HjmzJnDj3/8Y55++mmGDBnC559/TseOHWv8c/Lz84m26COGAoEAhYWF5OfnExUVZTqnHFvbbO0CO9vy8/PLvv4uK4uo666DMWPghOtNCRR+R0lRIQF/sVWPGdj5XJaytc3WLij/30GtOXU0d+5cp2XLls6NN97opKWlOWeccYaTnZ1d1x9XIxdddJEzZsyYctd17drVmThxYqW3LywsdHJzc8suO3fudABddNFFF10i+JKbm1vr+VPnYek4jjNx4kTH4/E4UVFRzr/+9a/6/Khq+f1+p2nTps4rr7xS7vq7777b+elPf1rpfaZOnWr8SdFFF1100cWuS12GZZ1ehv3222+5/fbb+ec//8nTTz/NqlWrGDRoEI888gh33HFHXX5ktQ4dOkRxcTHt2rUrd327du3Yt29fpfeZNGkSEyZMKPs+Ly+PlJQUtm3bdsq3vzS2QCDA22+/zcCBA6172cLWNlu7wM62L32PkvZ48KO2Xlq5nlatYw0XldcqCnZvyuHSS+15zMDO57KUrW22dgEcOXKELnX8YIA6Dctu3bqRmprK+vXrSU1NZfTo0SxevJg77riDN954gzfeeKNOMTXh8XjKfe84ToXrSnm93krPJhQXF0d8fHwo8uokEAgQHR1NfHy8db9ctrbZ2gUWtr33Hq1OOOI144LOVv3+Q/Axe/OrjfY8Zj+w7rk8ga1ttnYBFBcX1/m+dToadsyYMaxevZrU1NSy64YNG8Ynn3wSsvdXJiUl0bRp0wqryAMHDlRYbYrID556Ci64AEaPNl0i4mp1Gpa/+93vaNKk4l07dOhAdnZ2vaMq07x5c3r16lXh52dnZ9O3b9+Q/JkirubzwZEj0Lq16RIR16vxy7A7duyo1dszdu/ezRlnnFGnqKpMmDCBkSNH0rt3b9LS0pg3bx47duxgzJgxDfrniLheURGcey5cf73pEpGwUOOVZZ8+fRg9ejRr166t8ja5ubk888wzdOvWjVdeeaVBAk80bNgwZs+ejc/no0ePHqxevZo333yTTp06NfifJeJaPh/87W8alCINqMYryy+++IIHH3yQwYMHExUVRe/evWnfvj3R0dF8++23fP7552zatInevXvz6KOPMmTIkJAE33HHHSE74lbE9Z5+Ori96SazHSJhpsbDcteuXTz88MNkZWWxfPlyVq9ezfbt2/nuu+9ISkripptu4vLLL6dbt26h7BWRqmRnBz85JCbGdIlI2KnxsLzwwgvZt28fp512Gv/7v/9LTk4OiYmJoWwTkZry+YLbjAyzHSJhqsb7LOPj4/nqq68A2L59OyUlJSGLEpFaOHAguJrUSdFFQqbGK8vrrruO/v37k5ycjMfjoXfv3jRt2rTS25YOVREJsawsGDoUfvMb0yUiYa3Gw3LevHlce+21bN26lbvvvpvRo0fTWu/fEjFnxgxwHNBxAiIhV6vT3Q0ePBiAdevWMW7cOA1LEVP27oXrroOuXU2XiESEOp0bdv78+Q3dISI15fNBdDTcd5/pEpGIUafT3YmIIatWBbcalCKNqk4rSxExYM4cuOUW6N/fdIlIxNGwFHGD0vdRtmpltkMkQmlYitiuqAjOOQeGDTNdIhKxNCxFbObzwY9+BDfeaLpEJKLpAB8RW82dG9xqUIoYp5WliI3eeSd4ME/LlqZLRAQNSxH7ZGYGt+npZjtEpIyGpYhN9u2DFi10rlcRy2ifpYgtsrLgyBENShELaWUpYoPMzOBJ0c8913SJiFRCw1LEtH374Npr4bzzTJeISBU0LEVM8vmC+yjvvdd0iYicgvZZipjy9tvBrQaliPW0shQxYe7c4PsoBw40XSIiNaBhKdLYSk+KrhMOiLiGhqVIYyoq0rleRVxIw1KksWRmBj89RINSxHV0gI9IY5gzJ7j9xS/MdohInWhlKRJqq1YFD+bRBzeLuJZrVpYzZsygb9++xMTEEB8fbzpHpGZ8vuCw1KAUcTXXDMuioiJuuOEGfv3rX5tOEamZPXvA64UpU0yXiEg9ueZl2OnTpwOwYMECsyEip1AYKObdfx/k4Ovv8/+anU6zK26Bz/aazmLH/m9NJ4i4mmuGZV34/X78fn/Z93l5eQAEAgECgYCprApKW2xqKmVrm61dj761mT//6xtI+im8eyh4sUBJUWHZ17b9/oO9z6etXWBvm61dUL+msB6WM2fOLFuRnuidd94hJibGQNGpZWdnm06okq1ttnV9sul7IJoEr0Ncc9M1/1Fc5LDzh6/ffvttoqOjjfZUxbbns5StXWBvm41dBQUFdb6vx3EcpwFbamXatGmVDrMT5eTk0Lt377LvFyxYwPjx4zl69Gi1P7+ylWVKSgp79+4lMTGxzt0NLRAIkJ2dTUZGBlFRUaZzyrG1zcauJllZjC85m9cD8VzTuZgZt1xmTVt+fj5t2rQB4MCBA9YdJGfj8wn2doG9bbZ2ARw+fJjk5GRyc3OJjY2t1X2NrizvvPNOhg8ffsrbdO7cuc4/3+v14vV6K1wfFRVl3ZMI9naBvW3WdGVnQ9OmeLqeC5/sASxqg3IdNnWdzNY2W7vA3jYbu+rTY3RYJiUlkZSUZDJBpP7mzYORIyEjA15cb7pGRELANfssd+zYwZEjR9ixYwfFxcVs2LABgLPOOotWeg+bmJKZGdy2aGG2Q0RCyjXDcsqUKTz33HNl31944YVA8GCdAQMGGKqSiFZUBGeeCTfdZLpERELMNSclWLBgAY7jVLhoUIoRPh+8/roGpUiEcM2wFLHGU08Ft9ddZ7ZDRBqNa16GFbHCe+8FT4pey8PORcTdNCxFasrnC2779TPbISKNTsNSpCZ27YLmzWHiRNMlImKA9lmKVGfGDPjuOw1KkQimlaXIqWRmguPAj35kukREDNKwFKnKoUNw5ZXQo4fpEhExTMNSpDKZmdCyJUyYYLpERCygfZYiJ3vrreBWg1JEfqCVpciJnn0Wbr4ZBg82XSIiFtGwFClV+j5KSz8YWUTM0bAUAfD7oXPn4Nl5REROomEp4vPB+edrUIpIlXSAj0S2J58Mbq+5xmyHiFhNK0uJXB98AKNGQVyc6RIRsZyGpUSm0oN50tLMdoiIK2hYSuTZsQOiomDSJNMlIuIS2mcpkWXmTPj+ew1KEakVrSwlcmRmBrdnnmm2Q0RcR8NSIsORI3DFFdCzp+kSEXEhDUsJfz4ftG4N99xjukREXEr7LCW8LVsW3GpQikg9aGUp4esvf4ERI+DnPzddIiIup2Ep4UknRReRBqRhKeHH74eOHeHWW02XiEiY0LCU8OLzQY8eGpQi0qB0gI+EjyeeCG6vuspsh4iEHVcMy+3bt3PbbbeRmppKixYt6NKlC1OnTqWoqMh0mtgiJyd4UvQpU0yXiEgYcsXLsF9++SUlJSU8/fTTnHXWWXz22WeMHj2a/Px8Zs2aZTpPTCs9M0+fPmY7RCRsuWJYDh48mMGDB5d9f+aZZ7J582bmzp2rYRnptm+HZs10rlcRCSlXDMvK5ObmkpCQcMrb+P1+/H5/2fd5eXkABAIBAoFASPtqo7TFpqZSNraVlDjcu+RTPl13nD9+uR1PdF94fJXpLAD25BaWfW3TY3Zii22//2Dn7xnY2wX2ttnaBfVr8jiO4zRgS6PYtm0bPXv25LHHHuP222+v8nbTpk1j+vTpFa5fuHAhMTExoUyUEDr4HWRtsPvfebefU8z5Cfb8p1VYWMjw4cMBWLRoEdF6/6lEoIKCAkaMGEFubi6xsbG1uq/RYVnVMDtRTk4OvXv3Lvt+z5499O/fn/79+/Pss8+e8r6VrSxTUlLYu3cviYmJ9YtvQIFAgOzsbDIyMoiKijKdU46NbV9/tZdB8zfSvInDnBE9aNbMrsHZKsrDro1rGDTInscsPz+fNm3aAHDgwAHi4+PNBp3Ext8zsLcL7G2ztQvg8OHDJCcn12lYGv1b5s477yz7125VOnfuXPb1nj17SE9PJy0tjXnz5lX7871eL16vt8L1UVFR1j2JYG8XWNTm89GsZRLQiaYe6H9OOzu6ThAIBNj9mUWPGZTrsKnrZLa22doF9rbZ2FWfHqPDMikpiaSkpBrddvfu3aSnp9OrVy/mz59PkyaueNeLNKS//z24veUWeMyOfZQiEhnsev2qCnv27GHAgAF07NiRWbNmcfDgwbL/7fTTTzdYJo1mwQK48cbgCQcOHjddIyIRxhXDcsWKFWzdupWtW7fSoUOHcv+bC49PktoqPSl6JS+pi4g0Ble8lnnrrbfiOE6lFwlzhYXQoYPOzCMiRrliZSkRKjMTevaEX/3KdImIRDhXrCwlAs2eHdxecYXRDBER0MpSbPTxx8EjXqs5Q5OISGPRylLs4vPBsmUalCJiFa0sxR7btgVPij55sukSEZFytLIUO8ycCVFRGpQiYiWtLMW80vdRduxotkNEpAoalmJWbi5kZEBamukSEZEqaViKOT4fxMfD3XebLhEROSXtsxQzli4NbjUoRcQFtLKUxvf88zBsGFxzjekSEZEa0bCUxpWZGdw2b262Q0SkFjQspfEUFkJyMtx+u+kSEZFa0bCUxuHzwUUXaVCKiCvpAB8JvcceC24HDzbbISJSR1pZSmht2ACjRkFSkukSEZE608pSQsfng9df16AUEdfTylJCY8sWaNoUfvtb0yUiIvWmlaU0vIceghYtNChFJGxoZSkNq/Sk6B06mO0QEWlAGpbScI4dg4EDoV8/0yUiIg1Kw1IaRmYmJCTA2LGmS0REGpz2WUr9LVkS3GpQikiY0spS6ueFF+CGG+C660yXiIiEjIal1F3pwTw6KbqIhDkNS6mbggJo1w7+539Ml4iIhJyGpdSezwdpaRqUIhIxdICP1M6sWcFtRobZDhGRRuSaYXnVVVfRsWNHoqOjSU5OZuTIkezZs8d0VmTZuBFuuQWmTDFdIiLSqFwzLNPT03nppZfYvHkzS5YsYdu2bVx//fWmsyJGk6wsePVVaNvWdIqISKNzzT7Le+65p+zrTp06MXHiRIYOHUogECAqKspgWfgqDBTz7r8PsvnfR4hyEmhyzS/gs72ms9if5zedICIRxjXD8kRHjhzhhRdeoG/fvqcclH6/H7//P3+x5uXlARAIBAgEAiHvrKnSFpuaAB59azN//tc3QNvg5f8+Np1UThOPfY8Z2Pl8nthi2+8/2PmYgb1dYG+brV1QvyaP4zhOA7aE1P33389TTz1FQUEBl1xyCcuWLSMxMbHK20+bNo3p06dXuH7hwoXExMSEMjUsLP3HLla27EyC1yHOwrdS9koq4Senu+bX16jCwkKGDx8OwKJFi4iOjjZcJNL4CgoKGDFiBLm5ucTGxtbqvkaHZVXD7EQ5OTn07t0bgEOHDnHkyBG++eYbpk+fTlxcHMuWLcPj8VR638pWlikpKezdu/eUQ7axBQIBsrOzycjIsOcl5ePHmfDcGl7fV8I1nYuZcctl9rRh6WP2Axvb8vPzadOmDQAHDhwgPj7ebNBJbHzMwN4usLfN1i6Aw4cPk5ycXKdhafRl2DvvvLPsX7tV6dy5c9nXSUlJJCUlcfbZZ/Nf//VfpKSksGbNGtLS0iq9r9frxev1Vrg+KirKuicRLOry+SApCU+7NNgXPOLYmraT2NoFdrWd2GFT18lsbbO1C+xts7GrPj1Gh2Xp8KuL0gXxiStHaQCLFwe3d9wBL6432yIiYglXHOCzdu1a1q5dS79+/WjTpg1fffUVU6ZMoUuXLlWuKqUOXnwxeEJ0netVRKQcVwzLFi1a8MorrzB16lTy8/NJTk5m8ODBLFq0qNKXWaUOdFJ0EZEquWJYnn/++bz99tumM8JXfj6cdhr8+temS0RErOSaM/hIiPh88OGHGpQiIqegYRnJHn00uB040GyHiIjlXPEyrITA55/DyJFw+ummS0RErKeVZSTKzIRXXtGgFBGpIQ3LSPP55+DxwAMPmC4REXENDctI8uijkJCgQSkiUkvaZxkpSt9HqZdeRURqTcMyEuTnQ79+OupVRKSONCzDnc+nEw6IiNST9lmGsxdfDG41KEVE6kUry3C1eLFOii4i0kA0LMORToouItKgNCzDzfHjkJQU/DxKERFpENpnGU4yM2HdOg1KEZEGpmEZLh55JLjt399sh4hIGNLLsOHgyy+DJ0VPTjZdIiISlrSydDufD15+WYNSRCSENCzdbONGnRRdRKQRaFi61axZ0K4d/O53pktERMKe9lm6Uen7KNu2NdshIhIhNCzdpqAA0tIgI8N0iYhIxNCwdBOfL/gRW//936ZLREQiivZZusULLwS3GpQiIo1OK0s3WLIEbrhB53oVETFEK0vbZWbC559rUIqIGKSVpc2OHYOEBBg71nSJiEhE08rSVj4ffPKJBqWIiAU0LG300EPBbb9+ZjtERARw4bD0+/306NEDj8fDhg0bTOc0vC1b4OabYcoU0yUiIvID1w3L++67j/bt25vOCIkmWVnw0kvQoYPpFBEROYGrDvBZvnw5K1asYMmSJSxfvrza2/v9fvx+f9n3eXl5AAQCAQKBQMg6a6OkxOHeJZ/y8efFzCnuBvFt4fFVprMA2JNbWPa1LY9XqdIe27rAzrYTW2z6/S9l42MG9naBvW22dkH9mjyO4zgN2BIy+/fvp1evXrz66qskJSWRmprK+vXr6dGjR5X3mTZtGtOnT69w/cKFC4mJiQlhbc0d/A6yNtj9b5bbzynm/ARX/JpIFQoLCxk+fDgAixYtIjo62nCRSOMrKChgxIgR5ObmEhsbW6v7umJYOo7Dz372M3784x/zwAMPsH379hoNy8pWlikpKezdu5fExMRGKK/eN75ZXBboTvMmDnNG9KBZM7sGZ6soD7s2rmHQoAyioqJM55QJBAJkZ2eTkWFXF9jZlp+fT5s2bQA4cOAA8fHxZoNOYuNjBvZ2gb1ttnYBHD58mOTk5DoNS6N/M1e18jtRTk4O77//Pnl5eUyaNKlWP9/r9eL1eitcHxUVZceTWFhIkwt7wNoSmnqg/znt7Og6QSAQYPdnFj1mJ7G1C+xqO7HDpq6T2dpmaxfY22ZjV316jA7LO++8s+yloap07tyZrKws1qxZU2Hw9e7dm5tuuonnnnsulJmhkZkJyclw9XBYa8c+ShERqZzRYZmUlERSUlK1t3vyySfJysoq+37Pnj1cfvnlLF68mIsvvjiUiaHx/PPB7e23w8HjZltERKRadu0gq0LHjh3Lfd+qVSsAunTpQge3vc1i6VIYNkznehURcRHXvc/S1Xw+2LhRg1JExGVcsbI8WefOnXHBQbzl5eZCfDzcfbfpEhERqSWtLBuDzxf8mC0NShERV9KwDLWZM4PbtDSzHSIiUmeufBnWNbZtg5tugpMOUBIREXfRyjJUfD5YvFiDUkQkDGhYhsK6deDxwOTJpktERKQBaFg2tNmzITUVfvc70yUiItJAtM+yIWVmBrcJCWY7RESkQWlYNpTCQujZE664wnSJiIg0MA3LhuDzQYcO8KtfmS4REZEQ0D7L+lqwILjVoBQRCVtaWdbH3/8ON94IlXxmpoiIhA+tLOvK54MNGzQoRUQigFaWdXH0KMTFwbhxpktERKQRaGVZWz4f/PvfGpQiIhFEw7I2Sk+KftFFZjtERKRR6WXYmtq+PXgwT+fOpktERKSRaWVZE5mZ8OKLGpQiIhFKw7I6OTnB7aRJZjtERMQYvQx7Kk88AaNGQZ8+pktERMQgDcuq+HzBbXy80QwRETFPw7Iyfj/06AFXXWW6RERELKBheTKfDzp2hFtvNV0iIiKW0AE+J/rLX4JbDUoRETmBVpalli2DESMgOtp0iYiIWEYrSwi+9PrxxxqUIiJSKa0sjxyB2FgYP950iYiIWCqyV5aZmcHT2GlQiojIKbhmWHbu3BmPx1PuMnHixLr/wNKTovfs2TCBIiIStlz1MqzP52P06NFl37dq1apuP2jnThg2DM48s4HKREQknLlqWLZu3ZrTTz+93j/nncUraHXTSPhsbwNU1c/+PL/pBBERqYarhuXDDz9MZmYmKSkp3HDDDdx77700b968ytv7/X78/v8Mo9zcXADG57ajyZ/fC3lvbTjNHA4fPkxUVJTplHICgQAFBQXWtdnaBXa25efnl3195MgRiouLDdZUZONjBvZ2gb1ttnZB8HcfwHGc2t/ZcYnf//73zsqVK51PPvnEeeaZZ5ykpCTntttuO+V9pk6d6gC66KKLLrroUnbZtm1brWeQx3HqMmIbxrRp05g+ffopb5OTk0Pv3r0rXL9kyRKuv/56Dh06RGJiYqX3PXllefToUTp16sSOHTuIi4urX3wDysvLIyUlhZ07dxIbG2s6pxxb22ztAnvbbO0Ce9ts7QJ722ztguCrix07duTbb78lvpYfkmH0Zdg777yT4cOHn/I2nav4wOVLLrkEgK1bt1Y5LL1eL16vt8L1cXFx1j2JALGxsVZ2gb1ttnaBvW22doG9bbZ2gb1ttnYBNGlS+zeCGB2WSUlJJCUl1em+69evByA5Obkhk0RERCpwxQE+H3zwAWvWrCE9PZ24uDhycnK45557uOqqq+jYsaPpPBERCXOuGJZer5fFixczffp0/H4/nTp1YvTo0dx33321/jlTp06t9KVZk2ztAnvbbO0Ce9ts7QJ722ztAnvbbO2C+rUZPcBHRETEDVxzujsRERFTNCxFRESqoWEpIiJSDQ1LERGRakTssGzwj/wKAb/fT48ePfB4PGzYsMF0TtlbdaKjo0lOTmbkyJHs2bPHdBbbt2/ntttuIzU1lRYtWtClSxemTp1KUVGR6TRmzJhB3759iYmJqfUZQxranDlzSE1NJTo6ml69evHuu+8a7QFYvXo1V155Je3bt8fj8fDqq6+aTgJg5syZ9OnTh9atW9O2bVuGDh3K5s2bTWcxd+5cunfvXvaG/7S0NJYvX246q1IzZ87E4/Ew3vDnBU+bNq3C3/V1+UCOiB2WEPzIr71795ZdHnjgAdNJ5dx33320b9/edEaZ9PR0XnrpJTZv3sySJUvYtm0b119/veksvvzyS0pKSnj66afZtGkTjz/+OH/605+YPHmy6TSKioq44YYb+PWvf220Y/HixYwfP57f/va3rF+/np/85CcMGTKEHTt2GO3Kz8/nggsu4KmnnjLacbJVq1YxduxY1qxZQ3Z2Nt9//z2DBg0qd0J6Ezp06MBDDz3ERx99xEcffcTAgQO5+uqr2bRpk9Guk+Xk5DBv3jy6d+9uOgWA8847r9zf9Rs3bqz9D6nLSc3DQadOnZzHH3/cdEaV3nzzTadr167Opk2bHMBZv3696aQKXnvtNcfj8ThFRUWmUyp45JFHnNTUVNMZZebPn+/ExcUZ+/MvuugiZ8yYMeWu69q1qzNx4kRDRRUBztKlS01nVOrAgQMO4Kxatcp0SgVt2rRxnn32WdMZZY4dO+b86Ec/crKzs53+/fs748aNM9ozdepU54ILLqj3z4noleXDDz9MYmIiPXr0YMaMGVa8bAewf/9+Ro8ezfPPP09MTIzpnEodOXKEF154gb59+1r3MTwQPGFyQkKC6QwrFBUVsW7dOgYNGlTu+kGDBvH+++8bqnKX0o/3s+l3qri4mEWLFpGfn09aWprpnDJjx47liiuu4LLLLjOdUmbLli20b9+e1NRUhg8fzldffVXrn+GKM/iEwrhx4+jZsydt2rRh7dq1TJo0ia+//ppnn33WaJfjONx6662MGTOG3r17s337dqM9J7v//vt56qmnKCgo4JJLLmHZsmWmkyrYtm0bf/jDH3jsscdMp1jh0KFDFBcX065du3LXt2vXjn379hmqcg/HcZgwYQL9+vWjW7dupnPYuHEjaWlpFBYW0qpVK5YuXcq5555rOguARYsW8fHHH5OTk2M6pczFF1/MX//6V84++2z2799PVlYWffv2ZdOmTVV+CEel6r02tUhNPr8yJyen0vu+/PLLDuAcOnTIaNsTTzzh9O3b1/n+++8dx3Gcr7/+OqQvw9b2MTt48KCzefNmZ8WKFc6Pf/xj52c/+5lTUlJiRZvjOM7u3buds846q9rPOm3sLpMvw+7evdsBnPfff7/c9VlZWc4555xjpKkyWPoy7B133OF06tTJ2blzp+kUx3Ecx+/3O1u2bHFycnKciRMnOklJSc6mTZtMZzk7duxw2rZt62zYsKHsOhtehj3Z8ePHnXbt2jmPPfZYre4XVqe7O3ToEIcOHTrlbTp37kx0dHSF63fv3k2HDh1Ys2YNF198sbG24cOH8/rrr+PxeMquLy4upmnTptx0000899xzRroqe8x27dpFSkoK77//fkheBqpt2549e0hPT+fiiy9mwYIFdfoYnlB0ASxYsIDx48dz9OjRkDSdSlFRETExMfztb3/jmmuuKbt+3LhxbNiwgVWrVjV6U2U8Hg9Lly5l6NChplPK3HXXXbz66qusXr2a1NRU0zmVuuyyy+jSpQtPP/200Y5XX32Va665hqZNm5ZdV1xcjMfjoUmTJvj9/nL/m0kZGRmcddZZzJ07t8b3CauXYW3+yK+atj355JNkZWWVfb9nzx4uv/xyFi9eHJIhXp/HrPTfWSd+wHZDqk3b7t27SU9Pp1evXsyfPz9kg7K2XTZo3rw5vXr1Ijs7u9ywzM7O5uqrrzZYZi/HcbjrrrtYunQpK1eutHZQQrA1VP8N1sall15a4SjTX/7yl3Tt2pX777/fmkHp9/v54osv+MlPflKr+4XVsKwpmz/y6+Q/v1WrVgB06dKFDh06mEgCYO3ataxdu5Z+/frRpk0bvvrqK6ZMmUKXLl2MH1ywZ88eBgwYQMeOHZk1axYHDx4s+9/q8n6qhrRjxw6OHDnCjh07KC4uLnu/7FlnnVX23DaGCRMmMHLkSHr37k1aWhrz5s1jx44djBkzptEaKnP8+HG2bt1a9v3XX3/Nhg0bSEhIMPrf4tixY1m4cCGvvfYarVu3Ltu3GxcXR4sWLYx1TZ48mSFDhpCSksKxY8dYtGgRK1eu5K233jLWVKp169YV9um2bNmSxMREo/t6f/Ob33DllVfSsWNHDhw4QFZWFnl5eYwaNap2P6jhXxG237p165yLL77YiYuLc6Kjo51zzjnHmTp1qpOfn286rYJQ77OsqU8//dRJT093EhISHK/X63Tu3NkZM2aMs2vXLqNdjhPcH0gV+w5NGzVqVKVd77zzTqO3/PGPf3Q6derkNG/e3OnZs6cVb4N45513Kn18Ro0aZbSrqt+n+fPnG+361a9+VfYcnnbaac6ll17qrFixwmjTqdiwz3LYsGFOcnKyExUV5bRv39659tpr67SPN6z2WYqIiIRCRL/PUkREpCY0LEVERKqhYSkiIlINDUsREZFqaFiKiIhUQ8NSRESkGhqWIiIi1dCwFBERqYaGpYiISDU0LEVERKqhYSkiIlINDUuRMHfw4EFOP/10HnzwwbLrPvzwQ5o3b86KFSsMlom4h06kLhIB3nzzTYYOHcr7779P165dufDCC7niiiuYPXu26TQRV9CwFIkQY8eO5R//+Ad9+vThk08+IScnh+joaNNZIq6gYSkSIb777ju6devGzp07+eijj+jevbvpJBHX0D5LkQjx1VdfsWfPHkpKSvjmm29M54i4ilaWIhGgqKiIiy66iB49etC1a1d+//vfs3HjRtq1a2c6TcQVNCxFIsC9997Lyy+/zCeffEKrVq1IT0+ndevWLFu2zHSaiCvoZViRMLdy5Upmz57N888/T2xsLE2aNOH555/nvffeY+7cuabzRFxBK0sREZFqaGUpIiJSDQ1LERGRamhYioiIVEPDUkREpBoaliIiItXQsBQREamGhqWIiEg1NCxFRESqoWEpIiJSDQ1LERGRamhYioiIVOP/A0J3Ggt0L+zQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 向下取整函数\n",
    "f_array = np.floor(x_array)\n",
    "visualize_fx(x_array, f_array, '向下取整函数', True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cfa3bf58-0a6e-4ee6-981d-6680c7112db8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 向上取整函数\n",
    "f_array = np.ceil(x_array)\n",
    "visualize_fx(x_array, f_array, '向上取整函数', True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ff8bcf1e-6832-48d5-8b91-27a0dc3e1ba7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 符号函数\n",
    "f_array = np.sign(x_array)\n",
    "visualize_fx(x_array, f_array, '符号函数', True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4d97ec2e-03fa-42b3-bf57-7d0050af4790",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2e901584-7e40-4940-aaa3-60db8a936466",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 指数函数\n",
    "f_array = np.exp(x_array)\n",
    "visualize_fx(x_array, f_array, '指数函数')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c52b2d33-5759-48b1-bd02-47e67c4ecf81",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 对数函数\n",
    "x_array_ = np.copy(x_array)\n",
    "x_array_[x_array_<=0] = np.nan\n",
    "f_array = np.log(x_array_)\n",
    "visualize_fx(x_array_, f_array, '对数函数')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a6c9d69d-6bb0-4976-b9db-07e40e1f8f26",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2a76d332-aee9-4e69-b1d7-20b5eac340a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Repo: https://github.com/Visualize-ML\n",
    "# Book 1 Python for Beginners  |  From Basic Arithmetic to Machine Learning\n",
    "# Published and copyrighted by Tsinghua University Press\n",
    "# Beijing, China, 2023"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
